Sub-terahertz feedback interferometry and imaging with emitters in 130 nm BiCMOS technology

In this work, we present the effect of self-mixing in compact terahertz emitters implemented in a 130 nm SiGe BiCMOS technology. The devices are based on a differential Colpitts oscillator topology with optimized emission frequency at the fundamental harmonic. The radiation is out-coupled through the substrate side using a hyper-hemispheric silicon lens. The first source is optimized for 200 GHz and radiates up to 0.525 mW of propagating power. The second source emits up to 0.325 mW at 260 GHz. We demonstrate that in these devices, feedback radiation produces the change in bias current, the magnitude of which can reach up to several percent compared to the bias current itself, enabling feedback interferometric measurements. We demonstrate the applicability of feedback interferometry to perform coherent reflection-type raster-scan imaging.

There are different methods for generating THz radiation using electronic concepts.For example, the electrical nonlinearity of the electronic component can be exploited for frequency multiplication, or the amplifier with positive feedback can be used to create the oscillator.Depending on the nature of amplification and the peculiarities of implementation, exist various topographies of oscillators.
A typical schematic of the Colpitts oscillator in a common-collector configuration is presented in Fig. S1(a) 1 .The general functionality of an oscillator requires only a single amplifying element (it can be either a bipolar transistor or a field-effect transistor), one inductor L B , and two capacitances C 1 and C 2 .The oscillation frequency is defined by the resonant circuit formed by the inductor and the capacitance value resulting from the in-series connection of capacitances C 1 and C 2 : One of the critical aspects of the simple circuit, as presented in Fig. S1(a), is a requirement for a voltage gain to exceed 4 to sustain stable oscillations.However, this requirement can be eased by implementing a differential topology with two transistors M 1 and M 2 as presented in Fig. S1(b).
The differential circuit implementation has several advantages.First, it allows to sum on the power of two identical oscillators or extend the bandwidth by the asymmetry of sub-circuits as they can operate independently.Second, it provides a virtual ground along the symmetry axis, which can be used to bias the oscillators 2 .Furthermore, the oscillator analysis can be simplified into a one-port device treatment.The illustrative simulation of the real part of complex conductance between collector terminals is shown in Fig. S1(c).In simulations, the value of C E was fixed to 12 fF, and the inductance L E -90 pH.Transistors M 1 and M 2 are two identical 4-finger devices from SG130G2 process.The value of C BE can be approximately estimated from technology typical 2.5 fF/µm 3 .The simulation shows that resonant frequency with the minimum negative conductivity can be effectively tuned from below 200 GHz to nearly 300 GHz by reducing the value of L B from 65 pH to 20 pH.Furthermore, the modelling indicate that one can directly use a resistive load between collector terminals to extract the radiation.In order to implement the oscillators, one has to design the main passive elements (capacitors and inductors) as well as optimize their interplay with transistors.We have selected to use 4-finger devices from IHP SG13G2 technology with f T and f max of 350 GHz/450 GHz.Fig. S2(a

Figure S1 .
Figure S1.a) A simplified schematic of the common-collector Colpitts oscillator.b) A differential Colpitts-type topology with a pair of bipolar transistors M 1 and M 2 , which can be interpreted as a one-port element with negative conductance.The elements C 1 are substituted with C E .To achieve the highest frequency operation, the capacitor C 2 can be omitted as its role can be taken by internal capacitance C BE .c) Simulated real part of complex conductance of the circuit shown in part (b).The value of C E is 12 fF, the inductance L E -90 pH.Transistors M 1 and M 2 are identical 4-finger devices from SG13G2 process.The simulation shows that resonant frequency with approximately similar minimal value of negative conductivity can be effectively tuned from below 200 GHz to nearly 300 GHz by reducing the value of L B from 65 pH to 20 pH.

Figure
Figure S2.a) Real and imaginary parts of simulated antenna impedance.The inset presents a 3D sketch of a modified bow-tie antenna used for both oscillators.b) Spectrum of the imaginary part of impedance for gate's inductive element and source's LC circuit for D#1 200 GHz device.c) Spectrum of the imaginary part of impedance for gate's inductive element and source's LC circuit for D#2 260 GHz device.
) presents the real and imaginary parts of simulated antenna impedance to be used to load the oscillator.It has a bow-tie form with the shorting element as presented by a 3D sketch shown in the inset of Fig. S2(a).The metallic connection of leaves of bow-tie lowers the real part of the impedance to 25-40 Ω above 200 GHz with about equal inductive contribution.The same antenna was used in both devices: D#1, which targeted fundamental oscillation frequency at 200 GHz, and D#2 at 260 GHz.The simulated spectrum of main reactive elements and their forms are presented in Fig. S2(b) and (c).We have designed two different implementations of circuits for emitter L E C E with comparable values of equivalent